502 Server Error encountered when deploying a .NET Core web app on Google Cloud’s GKE, utilizing OAuth 2.0 authentication.

It seems like you encountered a few challenges while setting up your Kubernetes environment with authentication using Google’s services, specifically through OAuth. Here are the solutions to each problem:

Default Endpoint Issue: The default endpoint for your HomeController was covered by an [Authorize] attribute and causing health checks in kubernetes backend not working correctly due to unauthorized access attempts during those initial requests before any user login occurred. To resolve this, you made two changes:
- Created a separate Login screen without the Authorize filter for Google’s OAuth 2.0 authentication flow. This ensured that users could authenticate with their Google accounts to gain access to your application (without being considered unautish by Kubernetes). Here is how it was set up in code:
```
app.UseEndpoints(endpoints => {
    endpoints.MapControllerRoute("default", "{controller=Login}/{action=Index}");
});
```
- Redirected OAuth requests to HTTPS instead of just using the default HTTP method, which was not secure:
```
public void ConfigureServices(IServiceCollection services) {
  // Other configurations...
  
    var forwardOptions = new ForwardedHeadersOptions() {
        ForwardedHeaders = ForwardedHeaders.XForwardedProto, 
        KnownNetworks = DnsMessageKnownProxies.GetKnownHostNames(),    
        KknownProxies = DnsMessageKnownProxies.GetKnownProxyNames() // Cleared previously known proxies for loopback servers only:
    };
```
}

By doing so, you ensured that OAuth requests are correctly forwarded to HTTPS and thus became securely redirecting users after Google authentication is completed on their behalf. This also resolved the health check issues with kubernetes because your application was now properly handling user authorization flows before accessing any protected resources within it (thanks in part due to clear configuration for known networks/proxies).

Remember that ensuring secure communication, especially when dealing with authentication and sensitive data exchange between different services like Kubernetes and Google Cloud Platform is essential. Always keep an eye on security best practices during development or troubleshooting such issues!